A circle in the xy-plane has equation (x + 6)2 + (y - 2)2 = 25. Which of the following points does NOT lie in the interior of the circle?

Question

A. (-7,3)

B. (-3,1)

C. (0,0)

D. (-3,5)

Answer 1

There are two approaches to this problem. The easiest one would be to graph the circle and see which point is outside the circle.

The second approach would be to plug the x and y values into the equation to see how the left side compares to the right side. If (x + 6)² + (y - 2)² < 25, the point is interior. If (x + 6)² + (y - 2)² > 25, the point is exterior.

For (-7, 3), (-7 + 6)² + (3 - 2)² = 2 < 25 so it is interior.

For (-3, 1), (-3 + 6)² + (1 - 2)² = 10 < 25 so it is interior.

For (0, 0), (0 + 6)² + (0 - 2)² = 40 > 25 so it is exterior.

For (-3, 5), (-3 + 6)² + (5 - 2)² = 18 < 25 so it is interior.

Point (0, 0) is not an interior point.